A method for automatically mounting pneumatic tires onto wheel rims using a handling robot has already proved to be very advantageous and is the subject-matter of patent application DE 10 2005 030 692.6. With this method the handling and mounting of the pneumatic tires takes place with the aid of a gripper that is attached to the pivoting arm or to the robot hand of the handling robot and which can grip and hold the pneumatic tires in a suitable manner. In this context it has already proved to be advantageous if the pneumatic tires are gripped at the outer circumference in the region of the tread by the gripper and if the pneumatic tire is supported at the gripper on a side wall. It is furthermore necessary for the gripper fingers or arms which surround the pneumatic tire to be moved synchronously towards and away from one another in such a way that the gripped pneumatic tires always pass in a defined centre position with respect to the gripper and thus also with respect to the robot hand. Furthermore, it should be possible to grip pneumatic tires with different outer diameters. Therefore, the gripper should be able to be used in a wide diameter range. The gripping movement of the gripper should take place as quickly as possible and the forces on the wheel holder should be variable.